Tutorial Notes on One-Party and Two-Party Gaussian States

Details Tutorial Notes on One-Party and Two-Party Gaussian States Tutorial Notes on One-Party and Two-Party Gaussian States

2003-07-28

arxiv.org/abs/quant-ph/0307196v2

International Journal of Quantum Information, Vol. 1, No. 2 (2003) 153-188

Physics

Quantum Physics

34 pages, 4 figures; final version

Scientific paper

Gaussian states -- or, more generally, Gaussian operators -- play an important role in Quantum Optics and Quantum Information Science, both in discussions about conceptual issues and in practical applications. We describe, in a tutorial manner, a systematic operator method for first characterizing such states and then investigating their properties. The central numerical quantities are the covariance matrix that specifies the characteristic function of the state, and the closely related matrices associated with Wigner's and Glauber's phase space functions. For pedagogical reasons, we restrict the discussion to one-dimensional and two-dimensional Gaussian states, for which we provide illustrating and instructive examples.

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